func TestRDPToEpsilonConversionClosedForm(t *testing.T) · rdp=0.25 at alpha=2, delta=1e-5: 0.25 + ln(1e5) / 1

Read the equation

This relation defines rdp in the source section “func TestRDPToEpsilonConversionClosedForm(t *testing.T) · rdp=0.25 at alpha=2, delta=1e-5: 0.25 + ln(1e5) / 1”. Uses logarithmic scaling; its base and the positivity of its argument matter. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided physical or cognitive meaning to them.

Terms & definitions

The recovered passage does not supply a separate symbol table. Read the source context for the notation used in this version; familiar letters may carry different meanings in other builds.

How it works

1. Read rdp as the quantity being defined or updated by this relation.

2. Uses logarithmic scaling; its base and the positivity of its argument matter.

3. Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.

Assumptions & limits

• This source expression was recovered from the pinned code revision. Its presence does not establish that the associated program was built, run, or scientifically validated.

Original context

		t.Fatalf("noise multiplier = %v, want 2", a.noiseMultiplier())
	}
}

// TestRDPToEpsilonConversionClosedForm pins the RDP to (epsilon, delta) conversion at one order against the
// hand computed closed form epsilon(alpha) = rdp(alpha) + log(1/delta) / (alpha - 1).
func TestRDPToEpsilonConversionClosedForm(t *testing.T) {
	// rdp=0.25 at alpha=2, delta=1e-5: 0.25 + ln(1e5) / 1 = 0.25 + 11.512925465 = 11.762925465.
	got := epsilonAtOrder(0.25, 2, 1e-5)
	want := 0.25 + math.Log(1/1e-5)/(2-1)
	if !almostEqual(got, want, 1e-12) {
		t.Fatalf("epsilonAtOrder(0.25, 2, 1e-5) = %v, want %v", got, want)
	}
	// A second independent point: rdp=5 at alpha=10, delta=1e-6: 5 + ln(1e6)/9.
	got2 := epsilonAtOrder(5, 10, 1e-6)
	want2 := 5 + math.Log(1/1e-6)/(10-1)
	if !almostEqual(got2, want2, 1e-12) {
		t.Fatalf("epsilonAtOrder(5, 10, 1e-6) = %v, want %v", got2, want2)

rdp=0.25 at alpha=2, delta=1e-5: 0.25 + ln(1e5) / 1 = 0.25 + 11.512925465 = 11.762925465.

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